On maps taking lines to plane curves

TL;DR

This paper classifies all cubic rational maps that transform lines into plane curves, completing the broader classification of planarizations, which are maps that send lines to plane curves.

Contribution

It provides a complete description of cubic rational maps that take lines to plane curves, advancing the understanding of planarizations.

Findings

Complete classification of cubic rational maps taking lines to plane curves

Resolution of the classification of all planarizations

Advancement in understanding maps from lines to plane curves

Abstract

We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.